Optimization of the observer motion for bearings-only target motion analysis

This paper deals with the optimization of the receiver trajectory for target motion analysis. The observations are made of estimated bearings. The problem consists of determining the sequence of controls (e.g. the receiver headings), which maximizes the cost functional. This cost functional is generally a functional of the Fisher information matrix (FIM). The determinant of the FIM matrix has all the desirable properties, except the monotonicity property. The analysis is very complicated. A large part of this paper is centered around approximations of the FIM determinants. Using them, it is shown that, under the long-range and bounded controls hypotheses, the sequence of controls lies in the general class of bang-bang controls. These results demonstrate the interest of manoeuvre diversity. More generally, they provide a general framework for optimizing the observer trajectory.